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Staff Working Paper/Document de travail du personnel — 2020-34

Last updated: August 27, 2020

Monetary Policy and Cross-Border Interbank Market Fragmentation: Lessons from the Crisis by Tobias S. Blattner1 and Jonathan M. Swarbrick2

1 European Central Bank Frankfurt am Main, Germany 60314 2 Canadian Economic Analysis Department Bank of Canada, Ottawa, Ontario, Canada K1A 0G9 jswarbrick@bankofcanada.ca

i

Acknowledgements The authors would like to thank Stephan Fahr for all his help on the project. Thanks also to Dominic Quint, Paul Levine, Cristiano Cantore and Raf Wouters for helpful suggestions. The paper was based on work written while Jonathan was a doctoral candidate; he gratefully acknowledges the financial support from the Economic and Social Research Council (grant number ES/J500148/1) received during this period. The views expressed in this paper are those of the authors. No responsibility for them should be attributed to the Bank of Canada, the European Central Bank or the Eurosystem.

ii

Abstract We present a two-country model featuring risky lending and cross-border interbank market frictions. We find that (i) the strength of the financial accelerator, when applied to banks operating under uncertainty in an interbank market, will critically depend on the economic and financial structure of the economy; (ii) adverse shocks to the real economy can be the source of banking crisis, causing an increase in interbank funding costs, aggravating the initial shock; and (iii) asset purchases and central bank long-term refinancing operations can be effective substitutes for, or supplements to, conventional monetary policy.

Bank topics: Credit and credit aggregates; Business fluctuations and cycles; International financial markets; Transmission of monetary policy; Monetary policy framework

JEL codes: E44, E52, F32, F36

Résumé Nous présentons un modèle à deux pays intégrant des prêts risqués et des frictions sur le marché interbancaire transfrontière. Nous constatons que : 1) l’importance de l’effet de l’accélérateur financier, appliqué aux banques qui effectuent des opérations sur le marché interbancaire en contexte d’incertitude, dépend essentiellement de la structure économique et financière; 2) les chocs défavorables qui ébranlent l’économie réelle peuvent entraîner une crise bancaire, ce qui fait augmenter les coûts de financement interbancaire, aggravant ainsi le choc initial; et 3) les achats d’actifs et les opérations de refinancement à long terme des banques centrales peuvent efficacement remplacer ou compléter la politique monétaire traditionnelle.

Sujets : Crédit et agrégats du crédit; Cycles et fluctuations économiques; Marchés financiers internationaux; Transmission de la politique monétaire; Cadre de la politique monétaire

Codes JEL : E44, E52, F32, F36

Non-technical summary

Motivation and question

After the global financial and the euro area sovereign debt crisis, the euro area went through

a time of financial fragmentation. Firms and households in southern Europe started to face

much higher borrowing costs than those in the northern core. A key channel at the heart of this

financial fragmentation was the interbank market.

In this article, we seek to answer three important questions:

1. How is monetary policy in a currency union affected when interbank market conditions

depend on the quality of banks’ balance sheets?

2. How do asymmetric shocks impact countries in a currency union when banks differentiate

between domestic and foreign borrowers in the interbank market?

3. How do the recent measures taken by central banks work in this environment?

Contributions

To answer these questions, we develop, calibrate and simulate a model of a currency union. In

the model, lending banks get funds from both domestic and foreign savings banks to refinance

mortgage and private-sector business loans; but this interbank lending is subject to both borrower

and country-specific risk. We add into this framework two unconventional monetary policy tools:

long-term refinancing operations and an asset purchasing programme.

Findings

For the first question, we find that the strength and at times the direction of the impact of

financial frictions on monetary policy depends on two things: the asset composition of lending

banks’ balance sheets as well as how much competition there is in the lending market, and the

share of saver households in the economy.

On the second question, we show that cross-border capital flows can be highly procyclical and

that the effectiveness of monetary policy can be weakened. After an adverse shock to the value

of assets in one country, the rate charged by foreign lenders in the common interbank market

will rise as domestic banks’ balance sheets deteriorate amid a fall in the collateral value. The

effort by the central bank to stimulate the (area-wide) economy by lowering the policy rate in

response to the initial shock is partially off-set by rising domestic spreads.

Finally, we find that providing long-term refinancing operations to banks makes monetary policy

more effective for each unit of stimulus. We also find that asset purchases can be an effective

substitute for, or complement to, reductions in the key policy rate by relaxing bank balance

sheets.

1 Introduction

In the years following the global financial and the euro area sovereign debt crisis, the process

of financial integration in the euro area moved into reverse as firms and households in the

southern European periphery started to face much higher borrowing costs than their counterparts

in the northern core. One of the key channels at the heart of this financial fragmentation

was the interbank market, where the costs of cross-border lending rose sharply, and volumes

fell dramatically, in particular in peripheral economies, thereby likely having contributed to

reinforcing the macroeconomic fallout from the sharp collapse in aggregate demand. Although

market segregation gradually receded over the past few years, probably also thanks to the actions

taken by the European Central Bank (ECB), normal market functioning has not yet been fully

restored. At face value, these facts contradict the predictions of standard open-economy models

in which complete financial markets can be expected to facilitate, rather than to mute, effective

risk-sharing and thereby help temper the adverse effects of asymmetric shocks.

Against this background, and with a view to improving our understanding of recent events, this

article analyses the role of frictions in the interbank market of a currency union and examines

how unconventional monetary policy measures may mitigate, or offset, the effects such frictions

may have on financial conditions and, ultimately, on output and inflation. To this aim, we

develop, calibrate and simulate a two-country dynamic stochastic general equilibrium (DSGE)

model in which lending banks obtain funds from both domestic and foreign savings banks to

refinance mortgage and private-sector business loans, but where interbank lending is subject to

both borrower and country-specific idiosyncratic risk. Using this framework, we show that (i)

the strength of the financial accelerator, when applied to banks operating under uncertainty

in an interbank market, will critically depend on the economic and financial structure of the

economy; (ii) adverse shocks to the real economy can be the source of banking crises, causing

an increase in the interbank funding costs, aggravating the initial shock; and (iii) asset purchase

policies and central bank long-term refinancing operations can both be an effective substitute,

or complement, to changes in the conventional monetary policy instrument.

The interbank market plays a pivotal role in the euro area. Its smooth functioning is central for

banks to cope efficiently with idiosyncratic liquidity shocks and to ensure a uniform transmission

of the common monetary policy stance. Frictions in the interbank market may blur the signal

coming from monetary policy and ultimately hamper its transmission. One reason why interbank

markets may not operate efficiently has to do with transaction costs: owing to the unsecured

lending nature of the market, and its over-the-counter (OTC) structure,1 trading relationships

are often plagued by asymmetric information, counterparty risk, and search and monitoring costs

(see e.g. Afonso et al. 2011, Flannery 1996). As a result, banks’ wholesale market funding costs

1Electronic trading accounted for less than 10% of total unsecured transactions in 2014 (ECB 2015).

1

may differ across the currency union, and some banks may face hard borrowing constraints, which

could affect both credit supply and the ultimate borrowing conditions of the non-financial sector.

This also means that interbank market rates may be insufficient to characterize the monetary

policy stance, even at times away from the effective lower bound.

These frictions are particularly relevant in cross-border transactions, where differences in banking

supervision up until the introduction of the Single Supervisory Mechanism (SSM) in 2014,2 the

state of the business cycle, insolvency laws or accounting standards may obfuscate the evaluation

of the creditworthiness of foreign banks and expose lenders to uncertain counterparty risk. Freixas

and Holthausen (2005) show that such market imperfections may cause liquidity shortages or the

payment of interest rate premia that reflect the adverse selection of borrowers across countries.

In crisis times, these effects may become even more visible. Using bank-to-bank loan-level data

from TARGET23, Abbassi et al. (2014) find that for the same borrower on the same trading

day, and after controlling for lender and borrower fixed effects, cross-border loans were up to 25

basis points more expensive than domestic loans in the first three months following the collapse

of the former investment bank Lehman Brothers in 2008. De Andoain et al. (2014) estimate

that the premium charged to banks in more stressed economies spiked even more dramatically,

reaching over 63 basis points. The presence of risk premia unrelated to the specific borrower

suggests that information asymmetry constraints are important and that factors other than direct

counterparty risks may also drive pricing behavior in interbank markets. Despite the empirical

studies quantifying the effects of financial fragmentation, the precise source of these cross-border

frictions remains an open question. A common view is that the risk of cross-border lending,

particular to stressed economies, was being reassessed in the presence of imperfect information.4

This view motivates the inclusion of an additional monitoring cost in the cross-border interbank

market that rises in the face of heightened risk.

Cross-border interbank lending has been and continues to be an important element of the financial

structure in the euro area. Prior to the outbreak of the global financial crisis, more than half of

the average daily turnover in the unsecured market was with non-domestic euro area counterparts

(ECB 2009a). Strong credit growth in parts of the euro area, buoyant financial innovation and

lax financial regulation all contributed to an increasing reliance on confidence-sensitive wholesale

funding, with banks in current account surplus countries providing funding to banks in current

account deficit countries (see van Rixtel and Gasperini 2013). After the outbreak of the crisis,

2Even after the introduction of the SSM, national competent authorities retain discretion in applying common

rules (see Nouy 2017).3TARGET2 is the Eurosystem’s payment and settlement system and carries out more than 90% of all fund

flows between pairs of credit institutions in the euro area.4Imperfect information in relation to growth potential and the future profitability of destination banks, and

with respect to the possible implications of the heightened sovereign risk (see Al-Eyd and Berkmen 2013, IMF

2013).

2

the share of cross-border interbank lending fell dramatically to just over 25% in 2013 before

recovering again to reach levels around 40% in 2014, the latest available figures according to the

ECB (ECB 2015).

These sharp variations in the funding structure of banks – broadly speaking the mix between

wholesale and deposit funding – may have had severe repercussions on their operations and their

willingness and ability to extend credit to the non-financial sector. Several empirical studies

document that banks whose liabilities are mainly sticky household deposits, which are often

protected by generous government insurance schemes, continued to lend in the aftermath of the

crisis, whereas banks that relied predominantly on debt funding fared worse (Cornett et al. 2011,

Ivashina and Scharfstein 2010, Demirguc-Kunt and Huizinga 2010). In other words, wholesale

funding, and cross-border funding in particular, makes banks more vulnerable to changes in

market financing conditions with possibly strong repercussions on bank lending. These studies

therefore tend to suggest that real shocks may be amplified, and financial shocks accelerated, by

banks’ structural recourse to wholesale financing.

Despite its empirical relevance, however, few efforts have been undertaken to study the main

mechanisms and propagation channels of the interbank market in a structural model of the

macroeconomy. Indeed, financing frictions were long absent in a general equilibrium context.

The dominance of the Modigliani-Miller theorem (1958) that the financing structure of a firm is

irrelevant for its value confined the analysis to real and nominal frictions in the wider economy

(Christiano et al. 2005, Smets and Wouters 2007). The seminal work by Bernanke et al. (1999)

and the subsequent contributions by Christiano et al. (2003, 2010, 2014) and Iacoviello (2005)

made financial factors acceptable, and even desirable, in workhorse general equilibrium models.

Their studies showed that asymmetric information, agency problems and borrowing constraints

are important factors in driving and amplifying business cycles.

Yet, less progress has been made in understanding the impact of the financing structure of banks

on lending conditions of the private sector and, hence, on aggregate output and inflation. In the

pioneering work of Bernanke et al. (1999) and Christiano et al. (2003), and in work that followed

(cf. Goodfriend and Mccallum 2007, De Graeve 2008, Christensen and Dib 2008), banks were

either relegated to act as simple intermediaries between savers and borrowers or were operating

under perfect competition.

It was only more recently that a more prominent role was given to banks in general equilibrium

models. Gerali et al. (2010) and Darracq Paries et al. (2011) illustrate the effects of imperfect

competition in the banking industry on credit spreads and show that changes in banks’ leverage

ratio can impact loan supply conditions. However, in these models, banks can obtain funding in

a frictionless interbank market at the rate set by the central bank. Others have made attempts to

model the interbank market more explicitly. Gertler and Kiyotaki (2010), building on Kiyotaki

3

and Moore (1997), introduce a borrowing constraint in the interbank market by assuming that

banks may divert borrowed assets for personal gain, causing a spread between lending and deposit

rates. In the face of an adverse shock, this spread widens, which raises the cost of credit of firms,

affecting real activity.

Dib (2010) and de Walque et al. (2010) include an interbank market in which, due to an im-

plicit enforceability problem, borrowing banks can choose an optimal level of default,5 and where

banks must hold a regulatory level of capital. Calibrated for the US economy, both papers show

that bank capital attenuates, rather than amplifies, the real effects of shocks in this framework.

Hilberg and Hollmayr (2011) incorporate a secured interbank market into an otherwise standard

DSGE model and study the impact of central bank collateral policy on interbank lending rates.

They show that a change in the haircut applied to central bank refinancing operations can be

effective in steering interbank rates, but that the presence of an interbank market also attenuates

the effects of conventional monetary policy. Similarly, Carrera and Vega (2012) model the inter-

actions between banks’ reserve requirements and interbank lending activity, which they assume is

costly due to monitoring costs. They find that an increase in required reserves increases demand

in the competitive interbank market and pushes up the interest rate charged on these operations

as lending banks will have to pay higher monitoring costs. Funding conditions in the interbank

market then trickle down to lending and deposit rates, affecting real activity. In the framework

of Carrera and Vega (2012), changes in reserve requirements are therefore qualitatively similar

to traditional changes in policy rates.

Cross-border interbank lending, by contrast, has been largely ignored so far in the literature. In

’t Veld and van Lelyveld (2014) examine the role of international capital flows in the boom-bust

cycle in Spain by allowing borrowing-constrained households to borrow directly from foreign

lenders. Using an estimated three-country model, they find that the convergence of interest

rates in Spain to the levels prevailing in other euro area Member States, a loosening of collateral

constraints as well as falling risk premia on Spanish housing and capital has fuelled the Spanish

housing boom. In similar spirit to our paper, Ueda (2012) studies the international propagation

of shocks in an open economy model in which banks lend both domestically and internationally.

Whereas intermediaries in our model face a single-layer credit constraint with two parts: a cross-

border cost of credit that increases in domestic risk, and the Bernanke et al. (1999) financial

accelerator; Ueda (2012) introduces nested credit constraints so both firms and intermediaries

face an external finance premium. The authors use this to assess the necessary conditions to

cause a global economic downturn, whereas we focus on the role of policy when cross-border

frictions are present. Poutineau and Vermandel (2015) model the banking sector explicitly in

a two-country DSGE model. Contrary to Quint and Rabanal (2014), who study the optimal

5That is, default is not related to banks’ own idiosyncratic risks but a choice variable subject to an exogenous

cost of default.

4

design of macro-prudential policies in the euro area in a two-country DSGE model, they allow

for cross-border lending to firms and banks. They find that cross-border loans amplify the

propagation of country-specific shocks. Drager and Proano (2015) also allow for cross-border

banking where an international wholesale branch is collecting deposits from across the currency

union and distributes them to retail banks in the two countries. Although their model does

not give rise to interbank flows, similar to Poutineau and Vermandel (2015), they find that

cross-border banking amplifies the effects of exogenous shocks in a currency union.

In this article, we try to bring the various strands of the literature together by incorporating

credit risk in the interbank market of a currency union in a New Keynesian two-country, two-

sector model with sticky prices, habits in consumption and investment adjustment costs. There

are two types of banks in each country: savings banks, which have excess liquidity that they

are willing to trade across borders in the interbank market, and lending banks, which operate

under a structural liquidity deficit and require funding that they can obtain from the unsecured

area-wide interbank market. Following the costly state verification framework of Bernanke et al.

(1999), lending banks face idiosyncratic loan return shocks that are unobservable from the point

of view of savings banks. A positive probability of default gives rise to an external finance

premium that depends on the leverage of the borrower.

In addition, lending banks face a risk premium when taking a position in the cross-border inter-

bank market. This second friction is in the same spirit as the external financial intermediation

premium in Christoffel et al. (2008), but tailored to the features of an interbank market: when

the risk in the domestic economy increases, foreign lenders demand a higher rate of interest vis-

a-vis the borrower from that country as counterparty risk rises, thereby driving a further wedge

between the policy rate and interbank lending rates.

We use our model to answer three important questions: (1) how is the transmission of monetary

policy in a currency union affected when financing conditions in the interbank market depend

on the quality of banks’ balance sheets; (2) how do asymmetric shocks to the value of assets

propagate through a currency union when savings banks differentiate between domestic and

foreign borrowers in the interbank market; and (3) how effective are some of the measures central

banks have taken in the recent past to address funding bottlenecks in the interbank market?

Regarding the first question, we find that our model exhibits the financial accelerator effect (see

Bernanke et al. 1999) in the face of a common monetary policy shock but that, compared to

previous findings in the literature, there are noticeable differences in the way our model can give

rise to changes in the transmission of monetary policy. In particular, compared to a situation

where the financial accelerator operates directly at the balance sheet of firms, the strength and at

times also the direction of propagation crucially depends on the share of saver households in the

economy, the asset composition of lending banks’ balance sheets and the degree of competition

5

in the lending market.

Regarding the second question, our model is able to replicate some of the key features of the

financial crisis that resulted in a segmented interbank market.6 We show that capital flows

resulting from international financial integration can be highly procyclical, fluctuating in response

to business cycles, thereby raising financial and economic fragility even before a crisis emerges,

mainly by fostering credit growth. This means that in the wake of an adverse shock to the value

of assets in one country, the rate charged by foreign lenders in the common interbank market will

rise as banks’ balance sheets deteriorate amid a fall in the collateral value. The increase in the

interbank funding cost of banks in this economy offsets, to some extent, the effort by the central

bank to stimulate the (area-wide) economy by lowering the policy rate in response to the initial

shock. That is, compared to a model without cross-border interbank lending, and contrary to

union-wide shocks, monetary policy will be less effective. Moreover, as foreign funding becomes

more expensive, the economy that draws the shock is forced to improve its trade balance more

sharply relative to the case without financial frictions.

Finally, we study the effectiveness of two of the ECB’s recent non-standard measures. We find

that providing long-term refinancing operations (LTROs) to banks increases the effectiveness of

monetary policy per unit of stimulus – that is, LTROs empower conventional monetary policy.

The second policy focuses on the ECB’s asset-backed securities purchase programme (ABSPP)

that is particularly well suited to study in our model economy. Although securitization is more

complex in practice, the ultimate effects of the ABSPP can be well approximated by assuming

that the central bank purchases risky loans directly from banks, thereby freeing up bank balance

sheet capacity and reducing their funding costs in the interbank market. We find that asset

purchases in the form of loans, either directly or through purchases of ABS, can be an effective

substitute, or complement, to reductions in the key policy rate.

The rest of the paper is organized as follows. Section 2 lays out the model setup. Section 3

discusses model calibration and section 4 presents numerical simulations, illustrating the role of

the interbank market in driving the dynamics of the model. Section 5 analyzes the effects of the

ECB’s policy measures, while section 6 offers some concluding remarks.

2 The Model

The model is made up of two economies that share a single currency and monetary policy. In

each economy there are two types of households, savers and borrowers, monopolistic competitive

6In our model we focus on loan return risk. Ultimately, the implications of our findings are more broad based

and less dependent on the ultimate source of risk. For example, the sharp increase in spreads paid by banks in

stressed Member States during the sovereign debt crisis (see e.g De Andoain et al. 2014) works through the same

channel, that is, a (perceived) deterioration in the quality of banks’ balance sheets.

6

firms, savings and lending banks as well as a fiscal authority. The two economies, of size n

and (1− n), trade in both non-durable consumption goods and financial services in the form of

interbank credit. In the following, we describe the decision-making problems of the economic

agents resident in the home economy. Unless otherwise stated, analogous conditions hold for the

foreign economy. The time notation refers to the period in which the value is determined.

2.1 Households

The household sector is made up of a mass λ ∈ [0, 1] of patient households with discount factor

β and (1− λ) of impatient households with discount factor βB < β. The patient households are

referred to as the savers and the impatient households as the borrowers.

2.1.1 Savers

The saver household h ∈ [0, λ] chooses the level of consumption of non-durable goods Ch,t, hours

worked Lh,t, the housing stock Dh,t, and bank deposit savings Sh,t to maximize its lifetime utility

Et∞∑s=0

βs% ln (Ch,t+s − κCt+s−1) + (1− %) ln(Dh,t+s−1)− L1+φ

h,t+s

1+φ

subject to the nominal budget constraint

PCt Ch,t + PDt (Dh,t − (1− δD)Dh,t−1) + Sh,t ≤ RSt−1Sh,t−1 +WtLh,t + πt − Tt,

where % determines the relative weight of non-durable consumption in the saver’s utility and κ

the degree of external habit formation in consumption. The parameter φ refers to the inverse

of the Frisch labour supply elasticity. PCt and PDt are the price indices for consumption and

housing goods respectively (see derivation below). δD ∈ (0, 1) denotes the depreciation rate of

housing. The saver can deposit his savings in domestic banks which pay the risk-free nominal

interest rate RSt . Finally, the saver provides labour at the flexible nominal wage rate Wt and

owns the stock of net wealth of the economy, except for housing that is in part also owned by

the borrower household, therefore receiving profits πt from the banking and corporate sector and

paying lump sum taxes Tt.

Because saver households have the same preferences over consumption, housing, labour, savings

and investment, and are assumed to have the same initial wealth, we focus on a representative

saver from now onwards and drop the h subscript. The saver household chooses the optimal

inter-temporal plan subject to the budget constraint, resulting in a set of familiar first-order

7

conditions that will hold in equilibrium:

1 = RSt Et

[Λt,t+1

ΠCt+1

](2.1)

λCt QDt = βEt

[λDt + (1− δD)QDt+1λ

Ct+1

](2.2)

wt =LφtλCt

, (2.3)

where λCt and λDt are the marginal utilities of consumption and housing respectively, and Λt,t+1 ≡βλCt+1

λCtis the real stochastic discount factor over the interval [t, t+ 1]. Because housing, Dh,t, is

chosen one period in advance, the marginal utility, λDt , is discounted by β. Equations (2.1) and

(2.2) are the Euler equations implied by the demand for domestic deposits and the demand for

housing respectively. The relative price of housing is given by QDt ≡PDtPCt

and inflation is defined

by ΠCt ≡ PCt /PCt−1. The real wage rate is given by wt = Wt/P

Ct , which is equal to the marginal

rate of substitution between labour and consumption in equilibrium (2.3).

2.1.2 Borrowers

Preferences of the borrowers are the same as those of the saver except for the difference in the

time discounting. Borrower household h ∈ [λ, 1] maximizes

Et∞∑s=0

βsB

% ln(CBh,t+s − κCBt+s−1) + (1− %) ln(DB

h,t+s−1)− (LBh,t+s)1+φ

1+φ

,

subject to the nominal budget constraint

PCt CBh,t + PDt

(DBh,t − (1− δD)DB

h,t−1

)+RMt−1CR

HHh,t−1 ≤ CRHHh,t +WtL

Bh,t.

The notations are identical to the saver household and where the superscript B characterizes

variables specific to borrowers. Following Kiyotaki and Moore (1997) and Iacoviello (2005),

borrowers finance their consumption of housing with credit CRHHh,t obtained from lending banks

at the mortgage rate RMh,t. Banks impose collateral constraints of the form

CRHHh,t ≤ mEt[PDt+1

]DBh,t

1

RMt.

That is, banks will only lend to the point that total repayment is a fraction m of the expected

housing value, with a view to ensuring that households will not default the following period.

Under uncertainty, the borrowers could self-insure in some states of the world by borrowing

below the limit to protect against the effects of adverse shocks. To avoid issues introduced by

occasionally binding constraints, we therefore follow Iacoviello (2005) and choose the parameter

m to minimize the probability of this occurring.

8

The decision-making problems of the representative borrower household lead to a labor supply

condition analogous to that of the saver household. The housing investment decision leads to an

Euler equation of the form

λC,Bt QDt = βEt[λD,Bt + (1− δD −m)QDt+1λ

C,Bt+1

]+ Et

[λC,Bt QDt+1

ΠCt,t+1

RMt

]m. (2.4)

This differs from that of the savers due to a wedge between the marginal utility of consumption

and the marginal benefit of housing, introduced by the borrowing constraint. In the case that

m = 0, so there is no constraint, the two expressions are analogous.

2.2 Firms

We introduce nominal rigidities in the price of consumption goods following Calvo (1983). To this

end, we assume there are two types of firms in the model economy: intermediate goods firms that

are price takers in perfect competition, and final goods firms that operate under monopolistic

competition. There is ‘price-stickiness’ introduced in the latter sector as only a fixed proportion

of firms is able to update prices each period.

2.2.1 Intermediate goods firms

Each intermediate goods producer purchases capital goods KDt and hires labour LDt to produce

a homogeneous output Yw,t subject to a Cobb-Douglas production function

Yw,t = AtZt(KDt−1)

α(LDt )

1−α,

where the superscript D indicates factor demand and At and Zt are, respectively, stationary

union-wide and country-specific total factor productivity shocks. Both are modelled as AR(1)

processes: aAt = ρAaAt−1 + εAt where at ≡ lnAt and with a normal i.i.d. shock εAt . There is an

equivalent process for zt ≡ lnZt. Taking the aggregate real wage index wt as given, the profit

maximization implies labour demand is given by

wt = (1− α)Pw,tPCt

Yw,tLDt

, (2.5)

where Pw,t is the price at which the output is sold to all final goods firms. This implies that

Pw,t/PCt = mct is the real marginal cost in the final goods sector. New capital is purchased from

capital producers at the end of the period at real price Qt. Due to the constant returns to scale

in production, capital is paid at the marginal product

rkt = αPw,tPCt

Yw,tKDt−1

. (2.6)

If capital depreciates at rate δK , it follows that the gross nominal return on capital is given by

RKt =rKt + (1− δK)QKt

QKt−1

ΠCt−1,t. (2.7)

9

The end-of-period capital purchase decision of firms will ensure the expected discounted gross

return on capital will equal the expected discounted cost of funds. We will return to this in the

discussion of the banking sector below.

2.2.2 Capital Producers

For convenience, and without loss of generality, we introduce perfectly competitive capital pro-

ducers that make new capital goods and sell to firms. Capital follows the law of motion

Kt = (1− δK)Kt−1 +

[1− S

(IKtIKt−1

)]IKt

where IKt is investment and, following Christiano et al. (2005), the function S(·) is increasing in

changes to investment, given by

S

(IKtIKt−1

)=ζK

2

(IKtIKt−1

− 1

)2

. (2.8)

The capital producers solve

maxIKt

Et∞∑s=0

Λt,t+s

(QKt+s

[1− S

(IKt+sIKt−1+s

)]IKt+s −

PPt+sPCt+s

IKt+s

),

where PPt is the domestic producer price and QKt the real price of capital. This leads to the

first-order condition

PPtPCt

= QKt

(1− ζK

2

(IKtIKt−1

− 1

)2

− ζK(IKtIKt−1

− 1

)IKtIKt−1

)

+ Et

[Λt,t+1Q

Kt+1ζ

K

(IKt+1

IKt− 1

)(IKt+1

IKt

)2]. (2.9)

2.2.3 Final Goods Producers

Each final goods producer firm j purchases output from the intermediate goods sector at price

Pw,t and converts it into a differentiated good sold at price PPt (j) to households, durable goods

producers and the fiscal authority. Summing the demand schedules from each buyer (see section

2.2.4) implies a total demand for good j given by

Yt (j) =

(PPt (j)

PPt

)−σYt.

where σ denotes the elasticity of substitution between the different varieties, assumed to be

identical across the currency union. Every period, each firm faces a fixed probability 1− ξ that

it will be able to update its price. Denoting the optimal price at time t for good j as P ∗t (j), the

firms allowed to reoptimize prices maximize expected discounted profits by solving

maxP∗t (j)

Et∞∑k=0

ξkΛt,t+kPCt+k

Yt+k (j) [P ∗t (j)− Pw,t+k] .

10

The solution to the price-setting problem yields a price P ∗t which is independent of the firm’s

history of prices and therefore optimal for all price setters. With real marginal cost given by

mct =Pw,tPCt

and producer price inflation denoted by ΠPt ≡

PPtPPt−1

, we can write this as

P ∗tPPt

=σ

σ − 1

Et∑∞k=0 ξ

kΛt,t+k

(ΠPt,t+k

)σYt+kmct+k

PPtPCt

Et∑∞k=0 ξ

kΛt,t+k

(ΠPt,t+k

)σ (ΠCt,t+k

)−1

Yt+k

.

Using the aggregate producer price index PPt and the fact that all resetting firms will choose the

same price, by the law of large numbers we can find the evolution of the price index as given by(PPt)1−σ

= ξ(PPt−1

)1−σ+ (1− ξ) (P ∗t )

1−σ. (2.10)

While the distribution of prices is not required to track the evolution of the aggregate price index,

it implies a loss of output due to dispersion in prices. Final output is given by Yt = Yw,t1

∆twhere

price dispersion is given by

∆t =1

J

J∑j−1

(PPt (j)

PPt

)−σfor non-optimizing firms j = 1, ..., J . As a proportion (1 − ξ) of firms will optimize prices in

period t and knowing that the distribution of non-optimized prices will be the same as the overall

distribution, price dispersion can be written as a law of motion:

∆t = ξΠσt ∆t−1 + (1− ξ)

(Ω1,t

Ω2,t

)−σ. (2.11)

2.2.4 Consumption Good Producers

Households purchase differentiated final goods and combine bundles of domestically produced

goods and aggregate imports to produce the final consumption bundle according to

Ct =

[(τC) 1θC H

θC−1

θCt +

(1− τC

) 1θC IM

θC−1

θCt

] θCθC−1

,

where τC can be interpreted as the degree of home bias in household consumption expenditures,

and θC is the elasticity of substitution between domestic and foreign produced goods (see Arm-

ington 1969). Ht and IMt are bundles of differentiated domestic and foreign-produced goods

which households combine into baskets of goods using

Ht =

(∫ 1

0

Ht(j)σ−1σ dj

) σσ−1

(2.12)

IMt =

(∫ 1

0

IMt(j∗)

σ−1σ dj∗

) σσ−1

, (2.13)

where the asterisk indicates variables of the foreign country. The households purchase good

Ht(j) from producer j ∈ (0, 1) at price PPt (j) to maximize (2.12) subject to total expenditure

11

PPt Ht =∫ 1

0PPt (j)Ht(j)dj, with an equivalent problem for imports IMt(j

∗). This leads to Dixit

and Stiglitz (1977) demand schedules

Ht (j) =

(PPt (j)

PPt

)−σHt (2.14)

IMt (j∗) =

(P IMt (j∗)

P IMt

)−σIMt. (2.15)

Equivalent conditions for the domestic demand of the investment good and government con-

sumption good hold. We assume no pricing to market, which implies that P IMt = PP∗

t . The

final goods firms take input prices as given and maximize their profits PCt Ct−PPt Ht−P IMt IMt.

Profit maximization yields the following demand schedules for the domestic bundle and aggregate

imports:

Ht = τC(PPtPCt

)−θCCt (2.16)

IMt = (1− τC)

(P IMtPCt

)−θCCt. (2.17)

This leads to the consumer price index PCt given by

PCt =[τC(PPt)1−θC

+ (1− τC)(P IMt

)1−θC] 11−θC . (2.18)

2.2.5 Housing Producers

The price of durable housing goods can differ from that of consumption goods due to the presence

of adjustment costs. To ensure that savers and borrowers observe the same house price, we let

housing good producers augment the existing total stock, DTt ≡ λDt + (1− λ)DB

t , according to

the following law of motion:

DTt = (1− δD)DT

t−1 +

[1− S

(IDtIDt−1

)]IDt , (2.19)

where we follow the same adjustment costs as faced in capital investment. The housing goods

producers solve

maxIDt

Et∞∑s=0

Λt,t+sPCt+s

(PDt+s

[1− S

(IDt+sIDt−1+s

)]IDt+s − PPt+sIDt+s

),

which leads to the first-order condition

PPtPCt

= QDt

(1− ζD

2

(IDtIDt−1

− 1

)2

− ζD(IDtIDt−1

− 1

)IDtIDt−1

)

+ Et

[Λt,t+1Q

Dt+1ζ

D

(IDt+1

IDt− 1

)(IDt+1

IDt

)2]. (2.20)

12

2.3 Financial Intermediation

There are two types of banks: savings banks that take deposits from domestic households and

lend in the currency union-wide interbank market and lending banks that provide loans to both

domestic firms and households and finance these using interbank borrowing and their own net

worth. A financial friction emerges due to idiosyncratic loan return shocks faced by lending

banks. Costly state verification leads to an external finance premium as in Bernanke et al.

(1999). In addition, in light of the empirical evidence that borrower banks often have to pay a

premium that reflects not borrower but country-specific risks when accessing the international

interbank market (cf. section 1), we add a further friction whereby cross-border interbank credit

faces additional monitoring costs that depend on the prevailing risk in the lending market.

Savings banks operate under perfect competition with free entry, but aggregate shocks can lead

to unexpected profits or losses. The banks are owned by the patient households who are paid

all bank profits, or recapitalize banks if and when necessary. Lending banks face idiosyncratic

shocks when extending credit to the real economy that are costly for creditors to observe. Lim-

ited liability implies that these banks earn profits in equilibrium. Lending banks are treated

slightly differently to savings banks in that they pay a fixed dividend rate to ensure they cannot

become fully self-funded, equivalent to the assumption of an exogenous exit rate or higher banker

discounting (see e.g. Bernanke et al. 1999, Gertler and Kiyotaki 2010). The friction implies that

equity is always more valuable than debt, without which banks would not pay dividends in equi-

librium. Another difference is that savings banks can access central bank credit whereas lending

banks cannot. This is in part motivated by the risk exposure and specialization of lending banks;

savings banks are well diversified and the central bank requires a proportion of safe assets as

collateral.

2.3.1 Lending Banks

There are many lending banks of unit mass indexed b ∈ [0, 1]. They extend credit CRt to the

non-financial sector, which they finance with domestic IBHt and cross-border IBFt interbank

borrowing and net worth Nt:

CRt = Nt + IBHt + IBFt , (2.21)

where, following Poutineau and Vermandel (2015), IBHt and IBFt are chosen to maximize a

constant elasticity of substitution (CES) Armington aggregator (see Armington 1969) of domestic

and foreign interbank borrowing

IBt =

[(τ IB

) 1θIB (IBHt )

θIB−1

θIB +(1− τ IB

) 1θIB (IBFt )

θIB−1

θIB

] θIBθIB−1

,

13

where τ IB can be interpreted as a home bias in interbank borrowing and θIB is the elasticity of

substitution between domestic and foreign borrowing.7 A non-zero θIB implies that domestic and

foreign interbank borrowing are not perfect substitutes, rendering differences in lending rates.

Maximization yields the following familiar demand schedules:

IBHt = τ IB

(RIB,Ht

RIBt

)−θIBIBt (2.22)

IBFt = (1− τ IB)

(RIB,Ft

RIBt

)−θIBIBt, (2.23)

where RIB,Ht is the lending rate on the domestic interbank market and RIB,Ft the rate on the

cross-border market. Using these demand schedules and RIBt IBt = RIB,Ht IBHt + RIB,Ft IBFt ,

composite interbank funding costs are given by

RIBt =

[τ IB

(RIB,Ht

)1−θIB+ (1− τ IB)

(RIB,Ft

)1−θIB] 1

1−θIB. (2.24)

When granting loans to the non-financial private sector, we assume that lending banks cannot

diversify risk in their loan portfolio and that they experience idiosyncratic loan return shocks

ωt(b) that affect the value of the asset side of their balance sheets.8 The shocks are log-normally

distributed, log(ωt(b)) ∼ N(−(σ2

ω,t/2), σ2ω,t

), with mean Et[ωt] = 1 and standard deviation σω,t,

which is time-varying and is modelled as an AR(1) process: log(σω,t) = (1 − ρσ) log(σω,ss) +

ρσ log(σω,t−1) + uω,t and uω,t ∼ N (0, σσ).

After aggregate and idiosyncratic shocks hit the economy, net worth of lending banks evolves

according to

Nt (b) = ωt (b)RCRt CRt−1 (b)−RIBt−1IBt−1 (b) , (2.25)

where RCRt is the ex post return on banks’ loan portfolio CRt. Limited liability implies that

if the realization of the shock is below a threshold value ωt, then the lending bank will default

on its interbank borrowing as they would otherwise be insolvent. This threshold value is found

when setting Nt (b) = 0:

ωt (b) =RIBt−1IBt−1 (b)

RCRt CRt−1 (b). (2.26)

The lending banks will pay the saver households a fixed dividend rate, investing all remaining

profits in their own net worth. It is assumed that a defaulting bank will exit but that for every

exiting bank, a new one enters and is given a small start-up fund by the other banks. This

ensures that the number of banks is held constant at any point in time. The idiosyncratic loan

return and default leads to a distribution of lending banks over all possible values of net worth.

7This setup provides incentive for banks to borrow from both domestic and foreign banks as observed in the

data and is analogous to preferences over domestic and foreign produced goods in the trade part of the model.8Thus allowing us to study imperfect diversification in a tractable way.

14

The loan portfolio is comprised of mortgage loans to households CRHHt and lending to firms CRFt .

The former are treated as nominal one-period bonds, whereas for the latter it is convenient to

consider it as state-contingent debt,9 offering ex post, gross, nominal return given by RKt as

defined above. The lending banks specify a contract for interbank funds subject to participation

constraints given in the following section. After detailing the solution to the savings banks’

problem, we discuss the contract that determines the demand for interbank credit and the supply

of credit to the non-financial private sector.

2.3.2 Savings Banks

A representative savings bank has access to the central bank’s liquidity providing operations

CBt, raises deposits St from patient households and extends both domestic IBHt and cross-

border IBF∗

t interbank loans:

St + CBt = IBHt + IBF∗

t . (2.27)

Solving the profit maximization problem,

maxIBHt ,IB

Ft ,St,CBt

Et∞∑s=0

Λt,t+sPCt+s

(RIB,Ht+s+1IB

Ht+s + RIB,Ft+s+1IB

Ft+s −RSt+sSt+s −Rt+sCBt+s

),

subject to the balance sheet, leads to the zero-arbitrage condition

Et[

Λt,t+1

PCt+1

RSt

]= Et

[Λt,t+1

PCt+1

RIBt+1

],

where RIBt is the ex post return on interbank lending, and the condition RSt = Rt under standard

one-period central bank finance, where Rt is the policy rate. The savings bank can only observe

the loan return of the lending bank if it pays a proportional monitoring fee µ. As shown in

Townsend (1979), the implication of this costly state verification is that the fee will only be paid

in the event of default, with all other debtors paying the same interest rate. Interbank lending

is subject to a participation constraint that accounts for the distribution of idiosyncratic shocks

drawn by lending banks and the aggregate state of the economy.

For the domestic market, the savings banks require the expected real return from granting each

interbank loan to be equal to their expected real funding rate, using the household Euler equation.

This can be written as

1 = Et[

Λt,t+1

ΠCt+1[1− F (ωt+1 (b) , σω,t+1)]RIB,Ht (b)

]+ Et

[Λt,t+1

ΠCt+1(1− µ)

∫ ωt+1(b)

0ωRCRt+1

CRt(b)

IBHt (b)+IBFt (b)dF (ω, σω,t+1)

], (2.28)

9As in Gertler and Kiyotaki (2010). This is equivalent to the firms using state-contingent debt to purchase

the capital themselves. It is natural to assume that debt contracts are state-contingent due to costless monitoring

and enforcement and the risk neutrality of the lender.

15

where F (ω (b) , σ) ≡∫ ω(b)

0f(ω; −σ

2

2 , σ2)dω is the cumulative density function up to ω (b), with

probability density function f(ω; −σ

2

2 , σ2)

. Note that this implies that the value F (ωt+1 (b) , σω,t+1)

is the probability of default. The first part of the term on the right-hand side of equation (2.28)

is the expected discounted return from the 1−F (·) non-defaulted loans, of which the agreed lend-

ing rate is RIB,Ht . The second part is the expected discounted recovered value of post-defaulted

loans, subject to the cost µ. The interbank loans are used to refinance non-financial sector loans

with a rate of return ωRCRt+1 where ω is the idiosyncratic loan return shock, noting that the lower

the leverage, CRt(b)

IBHt (b)+IBFt (b), the higher the return to the creditor. Equation (2.28) highlights the

central role that the leverage plays in determining the interest spread in the banking sector; the

more highly borrowers are leveraged, the higher the rate of default and the lower the expected

return from defaulters. Because all banks will choose the same leverage ratio, individual bank

net worth does not affect the interest rate paid on credit, and equation (2.28) will therefore also

hold if the index b is dropped, with the variables treated as the aggregate averages.10

When taking positions in the cross-border interbank market, we assume that savings banks incur

additional monitoring costs ΓIB,t that are increasing in the level of risk within the economy. Such

costs reflect factors such as asymmetric information, counterparty risk as well as differences in

cross-border macroeconomic conditions. Specifically, it is given by

ΓIB,t = ζσ

(σ∗ω,tσω− 1

), (2.29)

which causes an increase to the monitoring costs following a shock to the variance of the id-

iosyncratic loan return shock. That is, country-specific risk shocks will cause an increase in

the finance premium of borrowing banks in the cross-border interbank market.11 Therefore, the

participation constraint for international interbank loans can be expressed as

1 = Et[

Λt,t+1

ΠCt+1(1− ΓIB,t)

[1− F (ω∗t+1 (b) , σ∗ω,t+1)

]RIB,F,∗t (b)

]+ Et

[Λt,t+1

ΠCt+1(1− µ)

G(ω∗t+1(b),σ∗

ω,t+1)

ω∗t+1(b) RCR,∗t (b)

CR∗t (b)

IBH,∗t (b)+IBF,∗t (b)

], (2.30)

where G(ω∗t+1 (b) , σ∗ω,t+1) ≡∫ ωt(b)

0ωdF (ω, σt) and F bt = F (ωt (b) , σt). As with (2.28), the first

part of the right-hand side of equation (2.30) is the discounted value of non-defaulted interbank

loans, although this now includes the cross-border monitoring cost, ΓIB,t.12 This participation

10As banks are atomistic, Λt,t+1 is independent of the idiosynctratic shock ωt+1 (b) drawn by the bank, thus

implying irrelevance of Nt (b) and allowing aggregation.11A common view is that heightened country-specific costs were due to the reassessment of the risk of cross-

border lending, particular to stressed economies, occurring in the presence of imperfect information in relation to

growth potential and the future profitability of destination banks, and with respect to the possible implications

of the heightened sovereign risk (see Al-Eyd and Berkmen 2013, IMF 2013). The linear representation is a

parsimonious way to capture the impact of heightened uncertainty on borrowing costs. We have tried other

functional forms with a limited impact on the results.12As a reminder of notation, note that for most variables, an asterisk indicates the foreign country variables.

16

constraint implies a spread in the cross-border interbank marketRIB,F,∗t (b)

RStthat is a function of

the monitoring cost ΓIB,t, which itself is increasing in the standard deviation of the loan return

shock: a higher σω,t will increase the risks of default by making lower realization of ωt(b) more

likely.

2.3.3 Interbank Credit Market

To model the over-the-counter structure of the interbank market, we follow Bernanke et al. (1999)

in our treatment of the lending contract. The lending banks choose credit to the non-financial

private sector CRt, the volume of interbank lending IBHt and IBFt , and interest rates RIB,Ht

and RIB,Ft to maximize their expected real net worth. The banks pay a fraction (1− γ) of their

profits as a dividend, with the remaining surplus retained as internal equity finance. Substituting

in the expression for ωt+1, the problem is written as

maxXt

Et[

Λt,t+1

PCt+1γ [1−G (ωt+1)− (1− F (ωt+1)) ωt+1]RCRt+1CRt

], (2.31)

where Xt =CRt, IB

Ht , IB

Ft , R

IB,Ht , RIB,Ft

is a vector of controls, dropping the individual

bank index. The maximization is subject to the bank balance sheet equation (2.21), the interbank

demand equations (2.22) and (2.23), the composite interest rate (2.24), the loan-to-value equation

(2.26), and the saver bank participation constraints given in equations (2.28) and (2.30).

The solution to the contract problem yields a condition that determines the wedge between the

nominal risk-free rate RSt and the expected return from credit to the non-financial sector RCRt+1.

We can express this as

Et[RCRt+1

RSt

]= Et

[s

(RSt , R

IB,Ht , RIB,Ft ,Γ∗IB,t,

IBtCRt

, ωt+1, σω,t+1

)](2.32)

with key arguments given, although the nominal stochastic discount factors of both countries are

also arguments of function s. In this solution, which is given in full in the online appendix, the

expected real return to lending is equated with the real marginal cost of external finance. Because

the solution is a function of the leverage rather than the bank size, the contract interest rates

will be independent of the bank’s own history of shocks. As leverage increases, the capital-asset

ratio NtCRt

falls, the probability of default increases, and the marginal cost of borrowing rises.

This is the financial accelerator mechanism; if, for instance, an adverse shock reduces the net

worth of the banking sector, bank leverage will increase, and so will the credit wedge s, causing

a further deepening of the downturn.

For the variables corresponding to cross-border flows, the distinction is less clear. RIB,F∗

t and RIB,H∗

t are the

rates paid by foreign lending backs for foreign and home credit IBF∗

t and IBH∗

t . The participation constraint

(2.30) is for home savings banks so is discounted with the home stochastic discount factor, but depends on the

financial positions of foreign-based lending banks.

17

2.3.4 Firm and Household Credit

As discussed previously, firm loans are treated as equivalent to equity, and so the return on firm

credit is simply the gross return on capital, RKt , defined in equation (2.7). The repayment rate on

household credit is the contracted nominal rate RMt−1. In addition to the amount of total credit

extended determined by the solution to equation (2.31), the lending bank chooses to allocate

credit to mortgages and business loans to solve

maxCRHHt ,CRBt

Et∞∑s=0

Λt,t+sPCt+s

(RMt+s (1− λ)CRHHt+s +RKt+s+1CR

Bt+s

),

subject to CRt = (1− λ)CRHHt + CRBt and where CRBt = QKt Kt. The solution implies that

Et[

Λt,t+1

PCt+1

RCRt+1

]= Et

[Λt,t+1

PCt+1

RMt

]= Et

[Λt,t+1

PCt+1

RKt+1

]must hold in equilibrium.

2.4 Monetary Policy

The monetary authority sets the nominal short-term interest rate in response to deviations of the

consumer price inflation rate from the union-wide inflation target ΠEMU and off-trend output

growth

Rt =

[R

(ΠEMUt

ΠEMU

)ϕπ (Y EMUt

Y EMUt−1

)ϕy]1−ϕr

Rϕr

t−1 exp(εmt ) (2.33)

with weights ϕπ and ϕy attached to inflation and output growth respectively. There is inertia in

the rule governed by ϕr. The union-wide variables ΠEMUt and Y EMU

t are weighted averages of

the home and foreign country variables:

ΠEMUt =

PEMUt

PEMUt−1

=

(PCt)n (

PC∗

t

)1−n(PCt−1

)n (PC

∗t−1

)1−n (2.34)

Y EMUt = (Yt)

n(Y ∗t )

1−n.

With a single policy rate, the economy as presented to this point features a unit root stemming

from a single savings rate across both economies. As savers in both countries face the same

return on assets, long-run effects from transitory shocks would prevail. For instance, if one of

the economies were to draw a positive supply shock, its net foreign asset position would improve

and the economy will have a current account surplus that would persist in the long run, with a

permanent increase in the wealth of savers. To restore the stationary property of the model, we

assume, consistent with past modelling practice in open-economy models, that the central bank

applies a small premium on the refinancing rate that depends on the net foreign asset position

18

NFAt of the home country.13 The rates paid on central bank credit CBt are determined by

Rt = RPt − ϑt(

exp

[κNFAtPYt Yt

]− 1

),

where ϑt is a stationary mean one shock to the premium, and κ the premium elasticity. RPt = RPt∗

is the central policy rate, and Rt and R∗t the rates paid on central bank credit.

Central bank funds are in zero net supply, so if savings banks in the home country borrow from

the central bank, it follows that foreign country savings banks are depositors, and Rt > Rt∗.

The risk premium will cause the net foreign asset position of banks in each country to adjust

until NFAt = NFA∗t = 0 and Rt = R∗t . The structure of the premium implies that there will be

small positive profits in equilibrium which are transferred equally to savers in the union. In the

numerical simulations, we choose κ sufficiently low to allow the rates to be very close, generating

persistent effects of shocks while ensuring that the model is stationary.

2.5 Market clearing conditions

In each economy, the labour market is in equilibrium when total supply by households equals

the demand from intermediate good producers

LDt = λLt + (1− λ)LBt . (2.35)

The corresponding domestic capital market equilibrium condition is given by

KDt = Kt. (2.36)

Total demand for domestically produced goods include the demand from domestic households

HTt = λHt+(1− λ)HB

t , demand from foreign consumers XTt = λXt+(1− λ)XB

t , demand from

capital producers IKt

(1− ζK

(IKt /I

Kt−1 − 1

)2)and from housing good producers IDt

(1− ζD

(IDt /I

Dt−1 − 1

)2)which are net the adjustment costs, and demand by the government, which is given as a propor-

tion gt of output Yt. The implied real resource constraint is then

Yt = HTt +XT

t + IKt + IDt + gtYt, (2.37)

with gt following a stationary stochastic process. The net foreign asset position evolves according

to the following nominal law of motion:

IBF∗

t − IBFt − CBt = RIB,F∗

t IBF∗

t−1 −Rt−1CBt−1 − RIB,Ft IBFt−1 + TBt, (2.38)

where the trade balance is defined as

TBt = PPt Xt − P IMt IMt. (2.39)

13See Schmitt-Grohe and Uribe (2003) for a full discussion of the techniques used to remove the random walk

in open-economy models.

19

The bilateral terms of trade are given by

ToTt =P IMtPXt

(2.40)

and, as discussed previously, the central bank funds are in zero net supply worldwide, so

nCBt + (1− n)CB∗t = 0. (2.41)

3 Calibration and Parametrization

A number of the structural parameters of our model are calibrated with the aim of matching

key empirical first moments. Other parameters are based on previous estimates in the literature

(see Table 1).

On the household side, we fix the fraction of savers λ in each economy to 0.65, close to the estimate

obtained by Quint and Rabanal (2014). The annualized inflation target is set to 2%, and the

discount factor of savers (borrowers) β (βB) is chosen to be 0.995 (0.94), ensuring a nominal

steady-state annual return on risk-free savings of around 4%. External habit in consumption κ

is set at 0.564 according to estimates of Christoffel et al. (2008) for the euro area. The relative

share of non-durables in consumption % is calibrated to be 0.82 to target the output share of

housing investment. The inverse of the Frisch labour supply elasticity φ is parametrized to be

0.4 (cf. Quint and Rabanal 2014). The quasi-share of domestic goods in total consumption τC is

fixed at 0.75 to ensure a steady-state share of imports in consumption of 25%. The elasticity of

substitution between domestic goods and imports θC is set at 1.9 in line with Quint and Rabanal

(2014) estimates.

On the production side, we choose a value of 0.3 for the share of labour α in the Cobb-Douglas

production function. Capital depreciation δK and housing depreciation δD are assumed to be 10%

per annum. Adjustment costs ζK in capital investment are fixed at 5.2 (following estimations

in Christoffel et al. 2008), while those in housing investment (ζD) are set at 1.7 as estimated in

Quint and Rabanal (2014). The elasticity of substitution across the final goods σ is chosen so

as to ensure a steady-state mark-up of 1.35 and the Calvo parameter ξ is set to be 0.9, both in

line with estimates obtained by Christoffel et al. (2008).

On the banking side, savings banks’ monitoring costs, µ, are assumed to be 0.2 as in Quint and

Rabanal (2014) and Carlstrom and Fuerst (1997). For the borrowers’ loan-to-value ratio, we use

the estimated value of m = 0.55 from Iacoviello (2005). The steady-state standard deviation of

the loan return shock, σω, and the bank dividend payment rate, 1 − γ, are calibrated to 3.39

percentage points and 4.53% respectively to target a steady-state value of the loan-to-value ratio

of banks ω of 0.9, in line with typical industry leverage ratios. The default rate of banks is

calibrated to be around 0.4% in steady state, matching the average historical default rate in

20

Parameter Description Value

β Patient agent discount factor 0.995

βB Borrowers discount factor 0.94

% Utility weight of non-durable consumption 0.82

τC Home-bias in consumption 0.75

σ Elasticity of substitution across consumption varieties 3.86

σω Standard deviation of loan return shock 0.0339

γ Retained share of bank profits 0.947

τ IB Home-bias in interbank borrowing 0.75

g Steady-state G/Y 0.2

λ Fraction of savers 0.65

εC Habits formation 0.564

φ Inverse Frisch elasticity 0.4

θC Elasticity between domestic goods/imports 1.9

α Capital share of production 0.3

δK Capital depreciation rate 0.025

δD Housing depreciation rate 0.025

ζK Capital adjustment parameter 5.2

ζD Housing adjustment parameter 1.75

ξ Calvo parameter 0.9

µ Monitoring costs 0.2

m Borrowers LTV ratio 0.55

θIB Elasticity of substitution between domestic/cross-border interbank

credit

2

ζσ Cross-border interbank cost coefficient 0.01

ϕy Taylor rule response to output growth 0.15

ϕπ Taylor rule response to inflation 1.9

ϕr Taylor rule persistence 0.87

Π Inflation target 1.005

Table 1: Calibration and parametrization of model parameters.

the banking industry over the period 1970-2010, as well as an equilibrium spread for mortgage

and interbank loans of around 1.72 percentage points and 10 basis points respectively over the

policy rate, in line with typical measures of the average spreads (see e.g. ECB 2009b). The

share of cross-border intra-euro area interbank borrowing τ IB is set at 0.75 to match figures

reported by Colangelo and Lenza (2013). The elasticity of substitution between domestic and

foreign interbank funding θIB is fixed at 2, implying that these sources of funding are not perfect

substitutes. This follows Poutineau and Vermandel (2015) who estimate the substitutability

of cross-border corporate loans between the eurozone core and periphery countries. The cross-

21

border interbank cost parameter, ζσ, we set to 0.01. For a 1-standard deviation risk shock,

ceterus paribus, bank default would increase from 0.1% to 0.25%, implying a rise in the cost,

ΓIB,t, of 0.1%.

On the policy side, we fix the share of government spending in GDP at 20%. Together with the

other parametrization of our model, this ensures that we are able to get close matches of the

relative spending shares of consumption (59%), investment (21%) and housing investment (4.5%)

in GDP with their empirical first moments for the euro area as a whole. Regarding monetary

policy, we follow Christoffel et al. (2008) and set the central bank response to inflation ϕπ to 1.9

and to output growth ϕy to 0.15. Policy inertia is set at 0.87.

Finally, the standard deviations and persistence coefficients of the shock processes are largely

taken from Christoffel et al. (2008), with the exception of the risk shock, which is taken from

Quint and Rabanal (2014), and the government spending shock, which has been calibrated on

the basis of estimates obtained by Smets and Wouters (2003). For the interbank risk premium

shock, for which no estimates in the literature are available, we assume a persistence of 0.8 and

a standard deviation of 0.2. These are shown in table 2.

Parameter Description Value

σA Technology shock 0.0126

σG Government spending shock 0.00325

σIB Interbank cost shock 0.2

σσ Risk shock 0.00339

σM Monetary policy shock 0.00115

ρA Technology shock 0.9

ρG Government spending shock 0.95

ρIB Interbank cost shock 0.8

ρσ Risk shock 0.85

Table 2: Parametrization of shock parameters.

4 Numerical Results and Analysis

To evaluate the model dynamics, we compute a second-order Taylor approximation of the decision

and transition functions and simulate impulse response functions.14 In a first step, we look at the

implication of our interbank market setup for the transmission of monetary policy by considering

14We used the dynare package to compute simulations (see Adjemian et al. 2011).

22

0 20 40

0

5

10

×10−3 Y EMU

0 20 40

0

5

10

15

×10−4 ΠEMU

0 20 40

-5

0

5

×10−3 IB

0 20 40

0

0.02

0.04

CRHH

0 20 40

-10

-5

0

5

×10−4 R

0 20 40

-4

-2

0

2

4

6

8

×10−3 s(·)

Baseline Fixed spreads Fewer Savers (λ = 0.5)

Figure 1: Impulse response functions to a negative monetary policy shock. s (·) is the external finance

premium. Relative deviations from the stochastic steady state except rates, which are in levels.

a standard monetary policy shock. In a second step, we analyze how frictions in the cross-

border interbank market may affect the dynamics of the economy in the face of country-specific

idiosyncratic shocks.

4.1 The interbank market and the transmission of monetary policy

Figure 1 shows the impulse responses of a number of variables to a reduction in the union-wide

policy rate and compares these to a modified version of our model in which the interbank frictions

are shut off, that is, the model collapses to one of complete financial markets where the spread

between bank lending rates and the policy rate is fixed to its steady-state value.

In both instances, the interest rate controlled by the monetary authority drops by about the

same amount initially. In our baseline model, however, the unanticipated reduction in interest

rates leads to an increase in the value of collateral held by lending banks. This, in turn, lowers

their funding costs in the interbank market as the perceived risk of default falls. Lending banks

operating under perfect competition will pass through the relief in funding costs to their final

customers, causing mortgage rates and financing costs faced by non-financial firms to drop by

23

more than the initial reduction in the key policy rate.

It is this additional fall in the borrowing conditions of households and firms that then leads to

more investment, more housing demand and, ultimately, higher domestic demand and inflation

in the currency union. In other words, like in Bernanke et al. (1999), the transmission of a

conventional change in monetary policy is more powerful in affecting broader macroeconomic

conditions. However, unlike in Bernanke et al. (1999), the amplification in transmission comes

directly from banks operating in an interbank market characterized by uncertainty on the part

of savings banks when extending short-term credit to counterparties in need of liquidity.

This implies that there are major differences to a situation where the financial accelerator op-

erates directly at the balance sheet of firms. The impact on aggregate demand, as well as the

strength of the pass-through of interbank conditions to final borrowing conditions, will ultimately

depend on three factors: the relative share of saver and borrower households in the economy, the

structure of lending banks’ balance sheets and the degree of competition in the lending market.

Starting with the latter, the less concentrated the lending market is, the stronger is the pass

through and the more pronounced are the effects on the real economy. That is, modifications

of our model along the lines of Gerali et al. (2010), introducing monopolistic competition in the

banking sector, can be expected to dampen the accelerator effect as banks would pass on lower

interbank funding costs at a pace slower than under our baseline model. Similarly, the larger the

share of bank lending to households, the larger the impact on output, given the role played by

private consumption in aggregate demand. And, finally, although the friction lowers borrowing

costs for firms and impatient households, Figure 1 also shows that the policymaker keeps the

interest rate higher relative to the fixed spread economy due to increased output and inflation.

Saver households hence face a higher savings rate, causing them to consume less non-durable and

durable goods in response. This effect offsets, to some extent, the increase in housing investment

coming from borrowers.

We illustrate this last point in 1: the red dashed line shows our baseline model, assuming,

however, a smaller share of savers λ=0.5. As expected, because the financial friction reduces

borrowing costs beyond the initial change in the policy rate, the more borrowers there are, the

larger the accelerator effect. Fewer savers, in turn, imply that the offset from a higher policy,

and hence savings rate, will also be smaller.

Overall, therefore, our simulations tend to suggest that, contrary to previous findings in the

literature (e.g. Hilberg and Hollmayr 2011), the presence of an interbank market can, and in

many circumstances is very likely to, amplify changes in the key policy rate. And although the

mechanism is similar to the well-known financial accelerator, there are noticeable differences in

the way our model setup can give rise to changes in the transmission of monetary policy.

24

4.2 Asymmetric shocks and cross-country spillovers

A key result of the previous section is that union-wide shocks will propagate differently through

the economy once financial frictions are allowed for and that it matters whether these frictions

are operating on the banking or the firm side. In this section we will focus on the implications

of our interbank market setup for the propagation and impact of idiosyncratic country-specific

shocks. Specifically, we look at how a positive shock to the variance of the idiosyncratic loan

return shock ω(b) will affect the behavior of banks in the cross-border interbank market and

analyze the footprint this will ultimately leave on aggregate demand.

Recall that savings banks incur additional monitoring costs when taking positions in the cross-

border interbank market. These costs are a function of the prevailing level of “economic” risk

(cf. equation 2.29). Therefore, a shock that raises the skewness of the distribution of ω(b) in

one country but not in the other, and hence increases the relative risk of bank default, will cause

savings banks to raise the risk premium they charge to borrowers resident in the economy hit by

the shock, even though the average loan return remains unchanged.

This can be seen in Figure 2: in our baseline model the funding rate in the cross-border interbank

market, RIB,Ft , increases by significantly more than compared to a model in which banks are

insensitive to both macroeconomic and counterparty risks.15 As a result, banks with a liquidity

deficit will partly substitute more expensive foreign borrowing with domestic borrowing, forcing

consumers to dial back more vigorously their imports in response. Naturally, this effect will be

stronger the more heavily the economy’s banking sector relies on cross-border interbank market

funding,(1− τ IB

), or, similarly, the more difficult it is to switch foreign with domestic funding

(θIB). This also means that, should countries differ in their financial structure, symmetric shocks

too can cause differences in banks’ funding costs across the currency union. For example, an

economy which predominantly finances loans to firms and households using funds from abroad

will see its overall funding costs increase more sharply in the face of an adverse shock, thereby

causing a steeper economic contraction than compared to an economy that mainly relies on

domestic funding. This stylized finding has been one of the key aspects of the crisis in peripheral

euro area economies: because many banks funded large parts of their liquidity needs abroad,

the sudden market freeze meant that aggregate imports fell drastically, thereby reinforcing the

macroeconomic fallout caused by the collapse in domestic demand and the rise in funding costs.

Cross-border monitoring costs are, however, only an amplifier of a natural response of our mod-

15To gain a sense of the magnitude of these deviations, note that the shock is scaled such that the annualized

probability of bank default increases by about 4% in the baseline model. This is close to the observed increase in

the expected default frequency of financial sector in the euro area in 2012 (see section 3.10 in European Central

Bank 2020). Output in the home country falls by around 0.5%, and less than 0.1% in the foreign economy. In the

data, real GDP in Spain and Italy fell by around 3% year-on-year in 2012, while in contrast, France and Germany

experienced only a slowdown.

25

Figure 2: Impulse response functions to a transitory risk shock in the home country, comparing baseline

model with a version with ζσ = 0. Relative deviations from the stochastic steady state except rates and

relative NFA, NFA/PCY , and the probability of bank default, F , which are in levels.

26

elling choice. As can be seen in Figure 2, banks resident in the foreign economy would have

increased their cross-border interbank rates even in the absence of these costs and despite a

measurable reduction in the union-wide monetary policy rate. The reason has to do with the

built-in increase in the risk of bank default: with output contracting in response to the shock,

domestic banks’ leverage rises, causing foreign banks to increase their lending rates.

What is more, with lending to the real economy having become riskier in the wake of the shock,

domestic savings banks too will ration their supply of interbank funds and will increase the

rate they charge on the remaining funds, causing a contraction in credit supply to the real

economy. The consequences are well-known: with credit less abundant and more expensive, both

households and firms reduce their investment and housing activities, amplifying the contraction

in aggregate demand that would have prevailed in the absence of frictions in the interbank

market.

The consequence is that interbank markets characterized by risky lending and costly state verifi-

cation have the potential to render monetary policy less effective by contributing to the fragmen-

tation of trades across borders, something that has become evident in the euro area during and

after the sovereign debt crisis. At that time, the transmission of the ECB’s monetary policy to

banks in the periphery had become severely impaired: although it cut its main refinancing rate

by 85 basis points between July 2012 and June 2014, bank lending rates to firms in Spain, for

example, fell only by some 20 basis points over the same period, reflecting, in part, effective credit

rationing in the (cross-border) interbank market. In response to these impairments, the ECB,

starting in June 2014, decided on a number of non-standard measures that aimed at restoring

the transmission of monetary policy. Some of these measures are the subject of our analysis in

the next section.

5 The effects of unconventional monetary policy

In this final section we ask whether recent non-standard monetary policy measures have been

able to overcome, or mitigate, frictions in the interbank market. The two policies we discuss are

long-term central bank refinancing operations and asset purchases.

5.1 Long-term refinancing operations

In our model economy, savings banks have access to funding from the central bank (cf. section

2.3.2). In addition to standard one-period loans to banks, in this policy exercise, the operations

of the central bank may take the form of multi-period loan contracts, similar to the ECB’s

LTROs.16 To prevent corner solutions whereby savings banks will choose only short-term or

16See e.g. https://www.ecb.europa.eu/press/pr/date/2011/html/pr111208_1.en.html for information on

this policy.

27

only long-term funding, the central bank sets a single target policy rate on multi-period bonds

and allows the short-term rate to be set via the zero-arbitrage condition. As discussed in section

2.3.2, the short-term central bank funds will be in zero net supply union-wide. This is also the

case with long-term funds. Indeed, in equilibrium, we will find that savings banks will not hold

long-term bonds at all; the availability of these loans is sufficient to introduce a wedge between

the policy rate on long-term refinance operations and the household saving rate.

To maintain tractability and keep the number of state variables manageable, we follow Rudebusch

and Swanson (2012)17 and introduce multi-period loan contracts using geometrically decaying

repayments over an infinite horizon. This setup reflects the aggregation of a large number of

loans at different points of repayment and of different maturities. As well as introducing just

one new state variable rather than potentially very many with long maturities, the appeal is

that using infinitely long loans with geometrically declining repayments allows us to control the

average maturity ψ ∈ [0, 1) with just one parameter, nesting the possibility of ψ = 0, in which

case it collapses to a standard one-period loan contract.

Every period t, a savings bank can take out a new loan CBt and agree to repay an infinite

number of declining payments such that the total amount due at period t is given by

CBTt−1 =

∞∑k=1

ψk−1RLTt−kCBt−k. (5.1)

When ψ > 0, RLTt is no longer equivalent to an interest rate. To analyze the role of the LTRO

policy, we assume that the central bank choosesRLTt so that the average interest rate on long-term

borrowing equals the policy rate Rt. As we are using perpetual loan repayments, we measure the

average duration using Macaulay’s duration of a stream of payments. It is then straightforward

to calculate the equivalent average nominal interest rate on the amount borrowed from the total

amount repaid. We find this leads to the following relationship between the rate RLTt and the

policy rate Rt:

Rt =

(RLTt1− ψ

)(1/d)

(5.2)

with average loan duration d = R/(R − ψ), where R is the steady-state policy rate.18 We can

then express equation (5.1) in recursive form as

CBTt = ψCBTt−1 +RLTt CBt. (5.3)

17Described in detail to analyze term premia on bonds in a working paper version of the article (see Rudebusch

and Swanson 2008). Used to introduce multi-period loan contracts in Benes and Lees (2010).18For perpetual loan repayments, the average loan duration is measured using Macaulay’s duration of a stream of

payments, given by dt =∑∞t=1 tPVt/

∑∞t=1 PVt where PVt is the present value of the cash flow (see e.g. Marrison

2002). Applying this to our example, we find in simulations that dt experiences only tiny fluctuations around

its steady-state value, and so we use the steady-state value as a close approximation. This can be simplified to

d =R

R− ψ. It is then straightforward to calculate the average interest rate given that borrowing is a convergent

series.

28

The important thing to note is that even if the bank does not borrow from the central bank in

equilibrium, as will be the case with purely symmetric shocks, the availability of these loans is

sufficient to have an important impact on the household saving rate, a point we will return to

later. Using equation 5.3 as a constraint in the profit maximization problem of the savings bank

leads to the following first-order conditions:

φt = Et[

Λt,t+1

ΠCt(1 + φt+1ψ)

](5.4)

φtRLTt = Et

[Λt,t+1

ΠCtRSt

]. (5.5)

This, with equation (5.2), gives the spread between the policy rate Rt and the deposit rate RSt .

φt is the real present value of the Lagrange multiplier on the law of motion of repayments due and

is a nominal pricing kernel for central bank credit. When d = 1 and ψ = 0, then RLTt = Rt = RSt

as in the standard model, and φt is just the nominal stochastic discount factor. As the loan

duration increases so ψ > 1, the implied future stream of payments increase and ψt >Λt,t+1

Πt,t+1.19

Figure 3 shows the LTROs at work, comparing the impulse response functions to the same risk

shock analyzed before, once with d = 1 and once with d = 16.20 This calibration mimics the four-

year loan duration of the ECB’s targeted LTROs introduced in 2014. The policy has two major

effects. First, in the face of an adverse shock, fewer cuts in policy rates are required to achieve the

equivalent stimulus in a multi-period loan economy. The reason is that the reduction in policy

rates lowers the average rate of interest for a longer period and hence further reduces the effective

present funding costs of forward-looking banks. That is, long-term refinancing operations with

fixed interest rates, such as the latest series of targeted LTROs, ensure planning certainty for

banks and thereby, in practice, provide major help with respect to maturity transformation

between longer-term lending and often short-term refinancing. And with banks immediately

passing on the additional funding cost relief to the ultimate borrowing conditions of households

and firms, policymakers are able to frontload required accommodation and thereby mitigate the

economic downturn.

The second interesting feature of LTROs is the asymmetric impact when economies are hit by

idiosyncratic shocks. As we argued before, once d > 1 (φt > 0), the deposit rate in each country

will no longer be fixed to the policy rate by the zero arbitrage condition. As equations (5.2)

and (5.5) highlight, the spread between the policy rate and the deposit rate depends on the

Lagrange multiplier, itself a function of the household stochastic discount factor. Specifically,

19One difficulty with our approach is that introducing the policy, or changing the average duration, during

a model simulation would cause the mapping between the repayment rate and the policy rate to be lost. For

example, the average loan duration stems from the continued existence of loans with a fixed parameter ψ. If ψ

were time varying, it would be considerably more difficult to compute the average loan duration or the average

rate across the loans. For this reason, we draw a comparison between a model in which the central bank provides

standard one-period credit and a long-term refinancing case with ψ > 0 and duration d > 1 fixed.20This corresponds to an average loan duration ψ of 0.9422.

29

Figure 3: Impulse response functions to a transitory risk shock with central bank with and without

LTRO policy response. Relative deviations from the stochastic steady state except rates, which are in

levels.

using equations (5.2) and (5.5) we can give the spread as

RtRSt

=Et[

Λt,t+1

ΠCt

][φt (1− ψ)]

1/d,

30

where

φt = Et[

Λt,t+1

ΠCt(1 + φt+1ψ)

].

So, asymmetric shocks will affect the spread differently in each country as a first-order effect.

From equations (5.4) and (5.5), a first-order approximation suggests that

RStEt [1 + φtψ]

=RSt∗

Et [1 + φ∗tψ].

In other words, if the expected path of the nominal stochastic discount factor is greater in the

domestic economy than in the foreign, then it follows that Etφt+1 > Etφ∗t+1, which implies that

RSt > RSt∗.

This can be seen in Figure 3. Because consumers in the foreign economy, following the shock,

expect a lower future marginal utility of consumption relative to the domestic country, LTROs,

by easing financial conditions abroad by more, are able to fully offset any negative spillovers of

the original shock to the rest of the currency union. Of course, the extent of the easing can differ

from shock to shock, but LTROs can generally be thought of as a powerful stabilization tool in a

currency union. This has been confirmed by recent ECB analysis (ECB 2017). They show that

from June 2014 to July 2015, i.e. after the first TLTRO operation, non-bidders in vulnerable and

non-vulnerable economies reduced their lending rates by about the same amount, while after the

second operation, in the period from March to December 2016, the reduction in lending rates

was larger in non-vulnerable economies, consistent with the predictions from our model. This

emphasizes that the sheer existence of the policy is enough to reduce financing conditions across

the currency union and, hence, to help central banks reach their price stability objectives.21

5.2 Asset Purchases

The second policy instrument we analyze is asset purchases by central banks, which became an

integral part of policymakers’ toolkit after, and in some jurisdictions even before, the outbreak

of the global financial crisis. Several attempts have been made in the literature to quantify

the effects of such purchases.22 On the theoretical front, Chen et al. (2012) and Gertler and

Karadi (2013) have recently made useful progress in capturing the effects of asset purchases on

the broader macroeconomy. In this paper, we want to focus on one element of the ECB’s asset

purchase programme that has received less attention in the literature and that is particularly

suited to study within the context of our model setup: its ABSPP.

The aim of this programme, launched in November 2014, is to facilitate credit provision to the

real economy by freeing up bank balance sheet capacity. Although the effects of securitization are

21We tried different parameter values in the Taylor rule and found the relative impact of the availability of

LTROs was unchanged.22For the United States see e.g. Krishnamurthy and Vissing-Jorgensen (2011) and Gagnon et al. (2011); for

the euro area see e.g. Blattner and Joyce (2016) and Altavilla et al. (2015).

31

more complex in practice, mainly related to regulation, the general idea behind this programme

can be illustrated by assuming that the central bank purchases assets directly from banks. Indeed,

one of the main reasons for banks to engage in securitization is balance sheet relief: securitization

typically involves a true sale of the underlying asset to a special purpose vehicle, removing assets

from the balance sheet and thereby reducing the amount of capital that a financial institution is

required to hold. We therefore follow Gertler and Karadi (2011) and treat asset purchases as if

the central bank lends directly to the private sector, which is a convenient shortcut to analyzing

the effects of the ECB’s ABSPP.

Specifically, the central bank issues one-period bonds at the market rate and uses the proceeds to

purchase a certain share Θt of loans from lending banks. Profits are distributed to the households

via lump sum transfers.23 The central bank budget constraint can be written as

Θt

(CRHHt + CRFt

)= BCBt (5.6)

Tt = RCRt Θt

(CRHHt−1 + CRFt−1

)−RSt−1B

CBt−1, (5.7)

where Tt are transfers to households and BCBt are central bank issued bonds. The first constraint

is that all funds raised are used to purchase assets and the second is that all profits are transferred

to households.

At the start of the period during which the asset purchase will take place, the policymaker

announces the purchase decision. This implies that the lending banks’ first-order conditions are

unchanged except for the volume of loans on banks’ balance sheets, which changes to

CRt = (1−Θt)(CRHHt + CRFt

).

With this in mind, we now examine how asset purchases can help stabilize the economy in the

face of an adverse shock, using again, for reasons of comparability, a risk shock in the domestic

economy. Figure 4 shows the general workings of a temporary asset purchase programme. In our

calibration the central bank is assumed to purchase 2% of all available assets in the first period,

in equal proportions across economies, and to hold them for four years. At this point, the assets

are gradually resold to the private sector, causing the central bank’s balance sheet to contract

by 2.5% every quarter.

The message is unambiguous: asset purchases in the form of loans, either directly or through

purchases of ABS, can be an effective substitute, or complement, to reductions in the key policy

rate. By reducing banks’ risk exposure to the real economy, policymakers are able to lower banks’

market-based funding needs and to compress their external finance premium in the interbank

market. Lower interbank funding costs, in turn, are passed on to households and firms, which

stimulates demand for loans and mortgages and, ultimately, investment and aggregate demand.

23Likewise, if there are losses, these are borne by households through lump-sum taxes.

32

Figure 4: Impulse response functions to a transitory risk shock with central bank asset-purchase policy

response. Relative deviations from the stochastic steady state except rates, net exports, PPX/P IMIM ,

and relative NFA, NFA/PCY , which are in levels.

As can be seen in Figure 4, in our example purchases of loans succeed in effectively mitigating the

fall in output and inflation without lowering the key policy rate. This means that, at the effective

lower bound, such a policy can be an effective complement to changes in the conventional policy

33

0 10 20 30 40

-3

-2

-1

0

×10−3 Y

0 10 20 30 40

-15

-10

-5

0

5×10−5 Π

0 10 20 30 40

-5

0

5

10

15×10−4 Y

∗

0 10 20 30 40

-10

-5

0

5

×10−5 Π∗

Baseline Asset Purchase Policy LTRO Policy

Figure 5: Impulse response functions to a transitory risk shock comparing central bank asset-purchase

policy response and LTROs. Y shows relative deviations from the stochastic steady state and Π shows

level deviation.

instrument. Note the interbank market lending volumes in Figure 4 mirror the asset purchases;

the central bank makes a large purchase in the first period, the assets are held for 4 years before

being gradually resold to the private sector.

Finally, in Figure 5, we perform a comparative analysis of the efficiency of our two unconventional

policy instruments to the same transitory risk shock. To ensure broad comparability, both policies

are calibrated to ensure the same target horizon of four years. The chart emphasizes that while

both policies can effectively mitigate the impact of adverse shocks on output and inflation, asset

purchases, even in relatively small size, are likely to be more powerful, reflecting the direct risk

transfer from private to public balance sheets. This means there is a trade-off for policymakers

between policy effectiveness and risk exposure. While an analysis of the optimal policy use goes

beyond the scope of this article, it may seem advisable to central banks to choose the optimal

policy mix depending on the severity and persistence of the shock, also bearing in mind that

very large adverse shocks may affect the supply side of the economy through hysteresis effects.

In these instances, policy may prefer to minimize the initial impact of the shock by choosing a

34

Figure 6: Welfare relative to baseline in period-by-period consumption equivalence terms. Conditional

on the impulse responses shown in Figure 5, for each period this shows value of the policy at time t in

terms of period t consumption.

policy that would re-establish quickly orderly trading conditions in interbank markets.

5.3 Welfare Considerations

Although the analysis of optimal policy is beyond the scope of this study, it is possible to compare

welfare outcomes conditional on the scenarios shown in Figure 5. We show the welfare of the

alternative policies relative to the baseline model in Figure 6. Welfare for each household is

defined as the discounted sum of future utility with total welfare given as the average, weighting

households by their population share. The figure gives this in consumption equivalence terms and

shows the period-by-period proportion of consumption that all households would give up in order

to be under the alternative policy framework.24 As this is a conditional welfare comparison, to

give a value for the effect of a policy programme on welfare we calculate the total value in terms

of annual consumption, finding that the asset purchase policy leads to total welfare gains of 2.7%

of a single year of consumption.25 The LTRO policy, in contrast, in the end leads to welfare

losses equivalent to 1.2% of annual consumption despite offering welfare gains in the short term.

This comparison does not give a full picture, as it assumes that the central bank has full freedom

to utilize conventional monetary policy. If this were not possible, because of the zero-lower bound

on nominal interest rates, for example, then the LTRO policy could be an effective substitute for

24To be a little more specific, each period, we solve W (Cbaselinet (1 + ξAt )) = W (CAPPt ) and W (Cbaselinet (1 +

ξBt )) = W (CLTROt ) for ξAt and ξBt , where Vt(i, j) = Ut(i, j)+β(i)Et [Vt+1(i, j)] for household of type i in country

i, and W averages V (i, j) weighting by population share.25The total period-by-period welfare gains add up to 2.7% of annual steady state consumption.

35

Figure 7: Welfare relative to baseline in period-by-period consumption equivalence terms conditional

on a risk shock and interest rates prevented from falling from 4 quarters. For each period this shows

value of the policy at time t in terms of period t consumption.

conventional interest rate adjustments. To illustrate this point, we repeat the exercise, only this

time preventing the interest rate from adjusting downward for four periods. The period-by-period

relative welfare for each policy is shown in Figure 7. This time, the LTRO policy offers total

welfare gains equivalent to 5% of annual consumption over the baseline case, highlighting the

value of credibly promising low-for-long interest rates. The asset purchase programme leads to

welfare gains equal to 13% of annual consumption, up from just 2.7%. Although an illustration,

the exercise indicates the potential of significant welfare gains from an expanded policy toolkit

when conventional policy is constrained.

6 Conclusion

Growing levels of excess liquidity in the wake of the ECB’s asset purchase programme, together

with attractive conditions attached to the ECB’s targeted longer-term refinancing operations,

have reduced the need of banks to seek funds in the euro area interbank market. Although

these measures have undoubtedly contributed to restoring the transmission of monetary policy,

and thereby to reinforcing the economic expansion the euro area has been enjoying since about

mid-2013, they also mask the prevailing fragilities related to the trading of central bank reserves

in a currency union characterized by structural differences across borders. Such differences may

lead to persistent cross-border capital flows intermediated, in part, by banks that are likely to

price interbank loans not only according to the credit quality of their counterparts, but taking

also into account differences in macroeconomic risk across euro area jurisdictions.

36

This article showed that such frictions in the interbank market may severely constrain the abil-

ity of monetary policymakers to achieve their area-wide price stability objective using merely

conventional policy instruments. In good times, credit frictions in the interbank market may

amplify changes in the key policy rate and contribute to boosting cross-border interbank loans,

creating risks of irrational exuberance. In bad times, pro-cyclicality in bank lending and pricing

may offset efforts by the central bank to stimulate the economy.

The good news is that the crisis has proven that unconventional policy measures can be highly

effective in overcoming frictions in the interbank market. The findings in this article confirm, by

and large, this intuition. In particular, long-term refinancing operations as well as asset purchase

programmes can complement, or substitute for, changes in the key policy rate and ease financial

conditions at a time when access to interbank credit might be restricted or excessively expensive.

This is especially true when there is restricted room to adjust the policy rates downward due,

for example, to the zero-lower bound on nominal interest rates. Limiting the recourse to such

facilities in future crises, however, requires a more forceful convergence in the growth capacities

of euro area economies, a task that lies beyond central bank mandates.

37

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